Journal of Statistical Theory and Applications

Volume 18, Issue 3, September 2019, Pages 244 - 258

A Multivariate Skew-Normal Mean-Variance Mixture Distribution and Its Application to Environmental Data with Outlying Observations

Authors
M. Tamandi1, *, N. Balakrishnan2, A. Jamalizadeh3, M. Amiri4
1 Department of Statistics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
2 Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada
3 Department of Statistics, Faculty of Mathematics and Computers, Shahid Bahonar University of Kerman, Kerman, Iran
4 Department of Statistics, Faculty of Basic Sciences, University of Hormozgan, Bandar Abbas, Iran
*Corresponding author. Email: tamandi@vru.ac.ir
Corresponding Author
M. Tamandi
Received 21 February 2019, Accepted 14 June 2019, Available Online 3 July 2019.
DOI
https://doi.org/10.2991/jsta.d.190617.001How to use a DOI?
Keywords
Multivariate distribution, Birnbaum–Saunders, ECM algorithm, Outliers, Mean-variance mixtures
Abstract

The presence of outliers, skewness, kurtosis, and dependency are well-known challenges while fitting distributions to many data sets. Developing multivariate distributions that can properly accomodate all these aspects has been the aim of several researchers. In this regard, we introduce here a new multivariate skew-normal mean-variance mixture based on Birnbaum–Saunders distribution. The resulting model is a good alternative to some skewed distributions, especially the skew-t model. The proposed model is quite flexible in terms of tail behavior and skewness, and also displays good performance in the presence of outliers. For the determination of maximum likelihood estimates, a computationally efficient Expectation-Conditional-Maximization (ECM) algorithm is developed. The performance of the proposed estimation methodology is illustrated through Monte Carlo simulation studies as well as with some real life examples.

Copyright
© 2019 The Authors. Published by Atlantis Press SARL.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Statistical Theory and Applications
Volume-Issue
18 - 3
Pages
244 - 258
Publication Date
2019/07
ISSN (Online)
2214-1766
ISSN (Print)
1538-7887
DOI
https://doi.org/10.2991/jsta.d.190617.001How to use a DOI?
Copyright
© 2019 The Authors. Published by Atlantis Press SARL.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - M. Tamandi
AU  - N. Balakrishnan
AU  - A. Jamalizadeh
AU  - M. Amiri
PY  - 2019
DA  - 2019/07
TI  - A Multivariate Skew-Normal Mean-Variance Mixture Distribution and Its Application to Environmental Data with Outlying Observations
JO  - Journal of Statistical Theory and Applications
SP  - 244
EP  - 258
VL  - 18
IS  - 3
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.d.190617.001
DO  - https://doi.org/10.2991/jsta.d.190617.001
ID  - Tamandi2019
ER  -